Photopgsfromfom 1.Epsf

Total Page：16

File Type：pdf, Size：1020Kb

Photo Gallery Pages Pierre Louis Moreau de Ma 1698- 1759. Courtesy of the BibliothGque Nationale, Paris, France. Leonhard Euler, 1707- 1783. E. T. Bell, Men of Mathemat- ics. Simon and Schuster, New York (1937). Joseph-Louis Lagrange, 1736- 18 13. Courtesy of the Bibliothhque Nationale, Paris, France. Pierre-Simon de Laplace, 1749- 1827. Courtesy of the Bibliothtque Nationale, Paris, France. Adrien Marie Legendre, 1752-1833. A. Legendre, with an introduction by K. Pearson, F. R.S. Tables of the Complete and Incomplete Elliptic Integrals. Cambridge University Press, Cambridge, England (1 934). Simeon-Denis Poisson, 178 1- 1840. Courtesy of the Biblioth6que Nationale, Paris, France. Carl Gustav Jakob Jacobi, 1804- 185 1. C. W. Borchart, C.G.J. Jacobi's Gesammelte Werke. Verlag Von G. Reimer, Berlin (1881). William Rowan Hamilton, 1805- 1865. Courtesy of the Royal Irish Academy. Joseph Liouville, 1809- 1882. L. J. Gino, Liouville and his Work. Scrip fa Math. 4: 147-154, 257-262 (1936). Georg Friedrich Bernhard Riemann, 1826-1866. Courtesy of the Deutsches Museum, Munich. Gaston Darboux, 1842- 19 17. G. Darboux, Eloges Acadkmiques et Discours Librairie Scientifique. A. Hermann et Fils, Paris (1912). Marius Sophus Lie, 1842- 1899. Included in Minkowski, H., Briefe an David Hilbert, Mit Beitragen und herausgegeben uon L. Rudenberg, H. Zassenhaus; Springer- Verlag, Heidelberg (1973). Gaston Darboux, 1842- 19 17. G. Darboux, Eloges Acadkmiques et Discours Librairie Scientifique. A. Hermann et Fils, Paris (1912). Marius Sophus Lie, 1842- 1899. Included in Minkowski, H., Briefe an David Hilbert, Mit Beitragen und herausgegeben uon L. Rudenberg, H. Zassenhaus; Springer- Verlag, Heidelberg (1973). Constantin CarathCodory, 1873- 1950. H. Tietze, Constantin Carathkodoiy. Archiv der Mathematik 2: 241-245 (1950). Edmond Taylor Whittaker, 1873- 1956. G. Temple, Edmond Taylor Whittaker, Biographical Memoirs of Fellows of the Royal Society 2: 299-325 (1956). Albert Einstein, 1879-1955. Courtesy of the Library of Congress, Washington, D.C., U.S.A . George David Birkhoff, 1884- 1944. G. D. Birkhoff; Collected Mathemti- cal Papers, American Mathematical Society, New York (1950). Elie Cartan, 1869- 195 1. Selecta, Jubilk Scientifque de M . Elie Cartan, Gauthier-Villars, Paris ('1 939). Amalie Emmy Noether, 1882- 1935. Constance Reid, Courant in Gottingen and New York. The Story of an Improbable Mathematician, Springer- Verlag, New York (1976). Carl Ludwig Siegel, 1896- . C 1,. Siegel, Gesammelte A bhandlungen, Springer- Verlag, Berlin (1966). Andrei Nikolaevic Kolmogorov, 1903- Photograph by Jiirgen Moser. Jiirgen Moser, 1928- . Photograph by Caroline A braham. Stephen 1930- . Photograph by Caroline Abraham. Vladimir I. -old, 1937- . Photograph by lurgen Moser. .

Copy Link

Recommended publications

The Cambridge Mathematical Journal and Its Descendants: the Linchpin of a Research Community in the Early and Mid-Victorian Age ✩
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 31 (2004) 455–497 www.elsevier.com/locate/hm The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age ✩ Tony Crilly ∗ Middlesex University Business School, Hendon, London NW4 4BT, UK Received 29 October 2002; revised 12 November 2003; accepted 8 March 2004 Abstract The Cambridge Mathematical Journal and its successors, the Cambridge and Dublin Mathematical Journal,and the Quarterly Journal of Pure and Applied Mathematics, were a vital link in the establishment of a research ethos in British mathematics in the period 1837–1870. From the beginning, the tension between academic objectives and economic viability shaped the often precarious existence of this line of communication between practitioners. Utilizing archival material, this paper presents episodes in the setting up and maintenance of these journals during their formative years. 2004 Elsevier Inc. All rights reserved. Résumé Dans la période 1837–1870, le Cambridge Mathematical Journal et les revues qui lui ont succédé, le Cambridge and Dublin Mathematical Journal et le Quarterly Journal of Pure and Applied Mathematics, ont joué un rôle essentiel pour promouvoir une culture de recherche dans les mathématiques britanniques. Dès le début, la tension entre les objectifs intellectuels et la rentabilité économique marqua l’existence, souvent précaire, de ce moyen de communication entre professionnels. Sur la base de documents d’archives, cet article présente les épisodes importants dans la création et l’existence de ces revues. 2004 Elsevier Inc.
[Show full text]
The Liouville Equation in Atmospheric Predictability
The Liouville Equation in Atmospheric Predictability Martin Ehrendorfer Institut fur¨ Meteorologie und Geophysik, Universitat¨ Innsbruck Innrain 52, A–6020 Innsbruck, Austria [email protected] 1 Introduction and Motivation It is widely recognized that weather forecasts made with dynamical models of the atmosphere are in- herently uncertain. Such uncertainty of forecasts produced with numerical weather prediction (NWP) models arises primarily from two sources: namely, from imperfect knowledge of the initial model condi- tions and from imperfections in the model formulation itself. The recognition of the potential importance of accurate initial model conditions and an accurate model formulation dates back to times even prior to operational NWP (Bjerknes 1904; Thompson 1957). In the context of NWP, the importance of these error sources in degrading the quality of forecasts was demonstrated to arise because errors introduced in atmospheric models, are, in general, growing (Lorenz 1982; Lorenz 1963; Lorenz 1993), which at the same time implies that the predictability of the atmosphere is subject to limitations (see, Errico et al. 2002). An example of the ampliﬁcation of small errors in the initial conditions, or, equivalently, the di- vergence of initially nearby trajectories is given in Fig. 1, for the system discussed by Lorenz (1984). The uncertainty introduced into forecasts through uncertain initial model conditions, and uncertainties in model formulations, has been the subject of numerous studies carried out in parallel to the continuous development of NWP models (e.g., Leith 1974; Epstein 1969; Palmer 2000). In addition to studying the intrinsic predictability of the atmosphere (e.g., Lorenz 1969a; Lorenz 1969b; Thompson 1985a; Thompson 1985b), efforts have been directed at the quantiﬁcation or predic- tion of forecast uncertainty that arises due to the sources of uncertainty mentioned above (see the review papers by Ehrendorfer 1997 and Palmer 2000, and Ehrendorfer 1999).
[Show full text]
The Tangled Tale of Phase Space David D Nolte, Purdue University
Purdue University From the SelectedWorks of David D Nolte Spring 2010 The Tangled Tale of Phase Space David D Nolte, Purdue University Available at: https://works.bepress.com/ddnolte/2/ Preview of Chapter 6: DD Nolte, Galileo Unbound (Oxford, 2018) The tangled tale of phase space David D. Nolte feature Phase space has been called one of the most powerful inventions of modern science. But its historical origins are clouded in a tangle of independent discovery and misattributions that persist today. David Nolte is a professor of physics at Purdue University in West Lafayette, Indiana. Figure 1. Phase space , a ubiquitous concept in physics, is espe- cially relevant in chaos and nonlinear dynamics. Trajectories in phase space are often plotted not in time but in space—as rst- return maps that show how trajectories intersect a region of phase space. Here, such a rst-return map is simulated by a so- called iterative Lozi mapping, (x, y) (1 + y − x/2, −x). Each color represents the multiple intersections of a single trajectory starting from dierent initial conditions. Hamiltonian Mechanics is geometry in phase space. ern physics (gure 1). The historical origins have been further —Vladimir I. Arnold (1978) obscured by overly generous attribution. In virtually every textbook on dynamics, classical or statistical, the rst refer- Listen to a gathering of scientists in a hallway or a ence to phase space is placed rmly in the hands of the French coee house, and you are certain to hear someone mention mathematician Joseph Liouville, usually with a citation of the phase space.
[Show full text]
Analogy in William Rowan Hamilton's New Algebra
Technical Communication Quarterly ISSN: 1057-2252 (Print) 1542-7625 (Online) Journal homepage: https://www.tandfonline.com/loi/htcq20 Analogy in William Rowan Hamilton's New Algebra Joseph Little & Maritza M. Branker To cite this article: Joseph Little & Maritza M. Branker (2012) Analogy in William Rowan Hamilton's New Algebra, Technical Communication Quarterly, 21:4, 277-289, DOI: 10.1080/10572252.2012.673955 To link to this article: https://doi.org/10.1080/10572252.2012.673955 Accepted author version posted online: 16 Mar 2012. Published online: 16 Mar 2012. Submit your article to this journal Article views: 158 Citing articles: 1 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=htcq20 Technical Communication Quarterly, 21: 277–289, 2012 Copyright # Association of Teachers of Technical Writing ISSN: 1057-2252 print/1542-7625 online DOI: 10.1080/10572252.2012.673955 Analogy in William Rowan Hamilton’s New Algebra Joseph Little and Maritza M. Branker Niagara University This essay offers the first analysis of analogy in research-level mathematics, taking as its case the 1837 treatise of William Rowan Hamilton. Analogy spatialized Hamilton’s key concepts—knowl- edge and time—in culturally familiar ways, creating an effective landscape for thinking about the new algebra. It also structurally aligned his theory with the real number system so his objects and operations would behave customarily, thus encompassing the old algebra while systematically bringing into existence the new. Keywords: algebra, analogy, mathematics, William Rowan Hamilton INTRODUCTION Studies of analogy in technical discourse have made important strides in the 30 years since Lakoff and Johnson (1980) ushered in the cognitive linguistic turn.
[Show full text]
Towards Energy Principles in the 18Th and 19Th Century – from D’Alembert to Gauss
Towards Energy Principles in the 18th and 19th Century { From D'Alembert to Gauss Ekkehard Ramm, Universität Stuttgart The present contribution describes the evolution of extremum principles in mechanics in the 18th and the first half of the 19th century. First the development of the 'Principle of Least Action' is recapitulated [1]: Maupertuis' (1698-1759) hypothesis that for any change in nature there is a quantity for this change, denoted as 'action', which is a minimum (1744/46); S. Koenig's contribution in 1750 against Maupertuis, president of the Prussian Academy of Science, delivering a counter example that a maximum may occur as well and most importantly presenting a copy of a letter written by Leibniz already in 1707 which describes Maupertuis' general principle but allowing for a minimum or maximum; Euler (1707-1783) heavily defended Maupertuis in this priority rights although he himself had discovered the principle before him. Next we refer to Jean Le Rond d'Alembert (1717-1783), member of the Paris Academy of Science since 1741. He described his principle of mechanics in his 'Traitéde dynamique' in 1743. It is remarkable that he was considered more a mathematician rather than a physicist; he himself 'believed mechanics to be based on metaphysical principles and not on experimental evidence' [2]. Ne- vertheless D'Alembert's Principle, expressing the dynamic equilibrium as the kinetic extension of the principle of virtual work, became in its Lagrangian ver- sion one of the most powerful contributions in mechanics. Briefly Hamilton's Principle, denoted as 'Law of Varying Action' by Sir William Rowan Hamilton (1805-1865), as the integral counterpart to d'Alembert's differential equation is also mentioned.
[Show full text]
2012 Summer Workshop, College of the Holy Cross Foundational Mathematics Concepts for the High School to College Transition
2012 Summer Workshop, College of the Holy Cross Foundational Mathematics Concepts for the High School to College Transition Day 9 { July 23, 2012 Summary of Graphs: Along the way, you have used several concepts that arise in the area of mathematics known as discrete mathematics or combinatorics. Here is a list of them: • Going from Amherst to the Mass Maritime academy is the equivalent of moving along a collection of edges in order from one vertex to another so that the vertex at the end of one edge is the vertex of the beginning of the next. This is called a path. • Starting at Worcester and ending at Worcester gives a path that starts at one vertex and ends at the same vertex. This is called a circuit or cycle. • A route that allows you to visit every school is called a Hamiltonian path (if it has a diﬀerent start and end points) or a Hamiltonian circuit (if it has the same starting and ending point). These are named after the 19th century British physicist, astronomer, and mathematician William Rowan Hamilton. Among other things, he is known for inventing his own system of numbers (can you imagine that!), called quarternions, which are important in mathematics and physics. Figure 1: The bridges of Konigsberg, Prussia. (Wikipedia, entry for Leonhard Euler.) • A route that allows you to drive every road between schools once is called an Eulerian path (if it has a diﬀerent starting and ending points) or a Eulerian circuit (if it has the same start and end point). These are named after the 18th century German mathematician and physicist Leonhard Euler.
[Show full text]
Leonhard Euler - Wikipedia, the Free Encyclopedia Page 1 of 14
Leonhard Euler - Wikipedia, the free encyclopedia Page 1 of 14 Leonhard Euler From Wikipedia, the free encyclopedia Leonhard Euler ( German pronunciation: [l]; English Leonhard Euler approximation, "Oiler" [1] 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[2] He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. [3] A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is our teacher in all things," which has also been translated as "Read Portrait by Emanuel Handmann 1756(?) Euler, read Euler, he is the master of us all." [4] Born 15 April 1707 Euler was featured on the sixth series of the Swiss 10- Basel, Switzerland franc banknote and on numerous Swiss, German, and Died Russian postage stamps. The asteroid 2002 Euler was 18 September 1783 (aged 76) named in his honor. He is also commemorated by the [OS: 7 September 1783] Lutheran Church on their Calendar of Saints on 24 St. Petersburg, Russia May – he was a devout Christian (and believer in Residence Prussia, Russia biblical inerrancy) who wrote apologetics and argued Switzerland [5] forcefully against the prominent atheists of his time.
[Show full text]
Siméon-Denis Poisson Mathematics in the Service of Science
S IMÉ ON-D E N I S P OISSON M ATHEMATICS I N T H E S ERVICE O F S CIENCE E XHIBITION AT THE MATHEMATICS LIBRARY U NIVE RSIT Y O F I L L I N O I S A T U RBANA - C HAMPAIGN A U G U S T 2014 Exhibition on display in the Mathematics Library of the University of Illinois at Urbana-Champaign 4 August to 14 August 2014 in association with the Poisson 2014 Conference and based on SIMEON-DENIS POISSON, LES MATHEMATIQUES AU SERVICE DE LA SCIENCE an exhibition at the Mathematics and Computer Science Research Library at the Université Pierre et Marie Curie in Paris (MIR at UPMC) 19 March to 19 June 2014 Cover Illustration: Portrait of Siméon-Denis Poisson by E. Marcellot, 1804 © Collections École Polytechnique Revised edition, February 2015 Siméon-Denis Poisson. Mathematics in the Service of Science—Exhibition at the Mathematics Library UIUC (2014) SIMÉON-DENIS POISSON (1781-1840) It is not too difficult to remember the important dates in Siméon-Denis Poisson’s life. He was seventeen in 1798 when he placed first on the entrance examination for the École Polytechnique, which the Revolution had created four years earlier. His subsequent career as a “teacher-scholar” spanned the years 1800-1840. His first publications appeared in the Journal de l’École Polytechnique in 1801, and he died in 1840. Assistant Professor at the École Polytechnique in 1802, he was named Professor in 1806, and then, in 1809, became a professor at the newly created Faculty of Sciences of the Université de Paris.
[Show full text]
Transcendental Numbers
INTRODUCTION TO TRANSCENDENTAL NUMBERS VO THANH HUAN Abstract. The study of transcendental numbers has developed into an enriching theory and constitutes an important part of mathematics. This report aims to give a quick overview about the theory of transcen- dental numbers and some of its recent developments. The main focus is on the proof that e is transcendental. The Hilbert's seventh problem will also be introduced. 1. Introduction Transcendental number theory is a branch of number theory that concerns about the transcendence and algebraicity of numbers. Dated back to the time of Euler or even earlier, it has developed into an enriching theory with many applications in mathematics, especially in the area of Diophantine equations. Whether there is any transcendental number is not an easy question to answer. The discovery of the first transcendental number by Liouville in 1851 sparked up an interest in the field and began a new era in the theory of transcendental number. In 1873, Charles Hermite succeeded in proving that e is transcendental. And within a decade, Lindemann established the tran- scendence of π in 1882, which led to the impossibility of the ancient Greek problem of squaring the circle. The theory has progressed significantly in recent years, with answer to the Hilbert's seventh problem and the discov- ery of a nontrivial lower bound for linear forms of logarithms of algebraic numbers. Although in 1874, the work of Georg Cantor demonstrated the ubiquity of transcendental numbers (which is quite surprising), finding one or proving existing numbers are transcendental may be extremely hard. In this report, we will focus on the proof that e is transcendental.
[Show full text]
ON THEOREMS of CENTRAL FORCES by William Rowan Hamilton
ON THEOREMS OF CENTRAL FORCES By William Rowan Hamilton (Proceedings of the Royal Irish Academy, 3 (1847), pp. 308–309.) Edited by David R. Wilkins 2000 On Theorems of Central Forces. By Sir William R. Hamilton. Communicated November 30, 1846. [Proceedings of the Royal Irish Academy, vol. 3 (1847), pp. 308–309.] Sir William R. Hamilton stated the following theorems of central forces, which he had proved by his calculus of quaternions, but which, as he remarked, might be also deduced from principles more elementary. If a body be attracted to a fixed point, with a force which varies directly as the distance from that point, and inversely as the cube of the distance from a fixed plane, the body will describe a conic section, of which the plane intersects the fixed plane in a straight line, which is the polar of the fixed point with respect to the conic section. And in like manner, if a material point be obliged to remain upon the surface of a given sphere, and be acted on by a force, of which the tangential component is constantly directed (along the surface) towards a fixed point or pole upon that surface, and varies directly as the sine of the arcual distance from that pole, and inversely as the cube of the sine of the arcual distance from a fixed great circle; then the material point will describe a spherical conic, with respect to which the fixed great circle will be the polar of the fixed point. Thus, a spherical conic would be described by a heavy point upon a sphere, if the vertical accelerating force were to vary inversely as the cube of the perpendicular and linear distance from a fixed plane passing through the centre.
[Show full text]
Verge 5 Barker.Pdf (420.0Kb)
Verge 5 Barker 1 by Daniel Barker t2 J = ∫ Ldt t1 ∂L ∂L − d = 0 dt & ∂qi ∂qi Verge 5 Barker 2 Finding the path of motion of a particle is a fundamental physical problem. Inside an inertial frame – a coordinate system that moves with constant velocity – the motion of a system is described by Newton’s Second Law: F = p& , where F is the total force acting on the particle and p& is the time derivative of the particle’s momentum. 1 Provided that the particle’s motion is not complicated and rectangular coordinates are used, then the equations of motion are fairly easy to obtain. In this case, the equations of motion are analytically solvable and the path of the particle can be found using matrix techniques. 2 Unfortunately, situations arise where it is difficult or impossible to obtain an explicit expression for all forces acting on a system. Therefore, a different approach to mechanics is desirable in order to circumvent the difficulties encountered when applying Newton’s laws. 3 The primary obstacle to finding equations of motion using the Newtonian technique is the vector nature of F. We would like to use an alternate formulation of mechanics that uses scalar quantities to derive the equations of motion. Lagrangian mechanics is one such formulation, which is based on Hamilton’s variational principle instead on Newton’s Second Law. 4 Hamilton’s principle – published in 1834 by William Rowan Hamilton – is a mathematical statement of the philosophical belief that the laws of nature obey a principle of economy. Under such a principle, particles follow paths that are extrema for some associated physical quantities.
[Show full text]
6A. Mathematics
19-th Century ROMANTIC AGE Mathematics Collected and edited by Prof. Zvi Kam, Weizmann Institute, Israel The 19th century is called “Romantic” because of the romantic trend in literature, music and arts opposing the rationalism of the 18th century. The romanticism adored individualism, folklore and nationalism and distanced itself from the universality of humanism and human spirit. Coming back to nature replaced the superiority of logics and reasoning human brain. In Literature: England-Lord byron, Percy Bysshe Shelly Germany –Johann Wolfgang von Goethe, Johann Christoph Friedrich von Schiller, Immanuel Kant. France – Jean-Jacques Rousseau, Alexandre Dumas (The Hunchback from Notre Dam), Victor Hugo (Les Miserable). Russia – Alexander Pushkin. Poland – Adam Mickiewicz (Pan Thaddeus) America – Fennimore Cooper (The last Mohican), Herman Melville (Moby Dick) In Music: Germany – Schumann, Mendelsohn, Brahms, Wagner. France – Berlioz, Offenbach, Meyerbeer, Massenet, Lalo, Ravel. Italy – Bellini, Donizetti, Rossini, Puccini, Verdi, Paganini. Hungary – List. Czech – Dvorak, Smetana. Poland – Chopin, Wieniawski. Russia – Mussorgsky. Finland – Sibelius. America – Gershwin. Painters: England – Turner, Constable. France – Delacroix. Spain – Goya. Economics: 1846 - The American Elias Howe Jr. builds the general purpose sawing machine, launching the clothing industry. 1848 – The communist manifest by Karl Marks & Friedrich Engels is published. Describes struggle between classes and replacement of Capitalism by Communism. But in the sciences, the Romantic era was very “practical”, and established in all fields the infrastructure for the modern sciences. In Mathematics – Differential and Integral Calculus, Logarithms. Theory of functions, defined over Euclidian spaces, developed the field of differential equations, the quantitative basis of physics. Matrix Algebra developed formalism for transformations in space and time, both orthonormal and distortive, preparing the way to Einstein’s relativity.
[Show full text]